From the hydraulic structures designer's point of view, the scour depth accurate estimation in downstream of spillways is so important. In this study, the scour depth was assessed downstream of ski-jump bucket spillways using two kernel based approaches namely Support Vector Machine (SVM) and Kernel Extreme Learning Machine (KELM). In the model developing process, two states were tested and the impacts of dimensional and non-dimensional parameters on model efficiency were assessed. The best applied model dependability was investigated via Monte Carlo uncertainty analysis. In addition, the model accuracy was compared with some available semi-theoretical formulas. It was observed that the applied models were more successful than available formulas. The sensitivity analysis results showed that q (unit discharge of spillway) variable in the state 1 and q²/[gY_t³] (g is gravity acceleration and Y_t is tail water depth) variable in the state 2 were the most significant parameters in the modeling process. Comparison among applied methods and one other intelligence approach showed that KELM was more successful in predicting process. The obtained results from uncertainty analysis indicated that the KELM model had an allowable degree of uncertainty in the scour depth modeling.